The present invention generally relates to signal processing, and particularly relates to signal interpolation processing.
A typical digital communication receiver converts baseband received analog signals as output by its “front-end” circuits into a corresponding discrete-time sequence of quantized values. According to the fundamental Nyquist criterion, sampling the baseband analog signal at or above twice its highest frequency allows the resulting discrete-time sequence to model the analog baseband signal with no loss of information.
However, practical digital signal processing algorithms, such as filtering, etc., may be implemented more easily if the analog baseband signal is over-sampled, meaning that the sampling rate used to generate the discrete-time sequence is above the Nyquist rate. For example, in a Wideband CDMA (WCMDA) signal processing context, the actual minimum sample rate equals 1.22 samples per “chip,” which translates into one discrete-time sample per 0.82 chips in the received signal. One sample per ¾ chips, however, offers a more practical, “digital friendly” minimum sampling reference given digital processing implementation considerations. With that minimum, receiver over-sampling rates include 2× over-sampling (“OS2”) at one sample per ½ chip, or 4× over-sampling (“OS4”) at one sample per ¼ chip.
Receiver architecture and operation at least partially determines the preferred over-sampling parameters. Consider, for example, Rake receiver structures, which represent a common receiver design in WCDMA systems. A Rake receiver despreads and combines multipath copies of a received signal to maximally utilize the signal energy available to the receiver. In a simplified model, each despreading “finger” in a Rake receiver processes a copy of the transmit signal corresponding to one radio propagation path, based on correlating the received signal—represented by a sampled discrete-time sequence—with an appropriately delayed reference spreading sequence. The Rake receiver then sums the correlation results (despread values) from each finger using a set of combining weights.
As a simplification, one may assume that the delay spacing of individual Rake fingers follows the Nyquist minimum and in a “practical” WCDMA Rake receiver application, a minimum distance of ¾ chips represents a convenient choice for minimum finger placement. With that minimum separation and assuming non-grid based finger placement, fingers may end up at any delay that is a ¼ chip multiple. With grid-based finger placement, where fingers are placed to cover regions of signal energy instead by being placed to match individual physical path delays, the finger delays fall at ¾ chip multiples.
Nonetheless, samples corresponding to the ¼ chip spacing must be produced to allow for the ¾ chip minimum spacing. One approach to obtaining the desired OS4 samples comprises up-sampling an OS2 sequence (inserting zeros for every second sample of the OS2 sequence) and applying a Finite Impulse Response (FIR) filter, consisting of a predetermined number of filter taps, at the OS4 rate. While the resulting OS4 sequence contains no additional information compared to the OS2 sequence, it does permit use of simple Rake structures to effect optimal demodulation of the received symbol sequence.
However, those skilled in the art will appreciate that, when grid-based finger placement is used, not all samples corresponding to all multiples of ¼ chips are necessarily used during despreading. Interpolating the OS2 sequence to obtain these ultimately unused samples represents needless processing overhead and is a waste of receiver power. Of course, the same issue arises with other grid spacing/phase parameters, and in non-grid placement as well.
Similar issues arise in chip equalizer and other fractionally spaced equalizer structures. Channel equalizers use knowledge of multipath channel characteristics (path delays and coefficients) to compensate for the loss of code orthogonality in a received CDMA caused by Inter-Symbol-lnterference (ISI). However, not all delays are used for a given (tap) delay resolution. Knowing how the propagation channel taps are spaced, which is learned from channel estimation processing, allows the receiver to pick a reduced number of equalizer channel taps for equalization processing. That is, one can formulate a reduced-tap channel equalizer for certain multipath channel realizations, and these reduced-count taps correspond only to a limited subset of samples from the over-sampled baseband signal. For example, assume possible channel equalization taps at (1, 1.25, 1.5, 1.75, 2.0, 2.25, . . . ) and a 4× over-sampled signal having phases (0, 1, 2, and 3). Further, assume that for current channel conditions, the equalizer taps at x.25 are not used (“x” equals 1, 2, . . . ). In this case, the “phase 1” samples in the over-sampled signal are unneeded and their computation in an interpolation filter represents wasted receiver processing.
More generally, many over-sampled signal generation applications include delay-based processing, wherein over-sampled signal samples corresponding to certain processing delays are used and other samples corresponding to other processing delays are not. Generating output values represents wasted receiver processing to the extent that the output values correspond to delays not of interest for subsequent processing of the over-sampled signal.